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Simplifying 25r2 + 5r + -2 = 6r Reorder the terms: -2 + 5r + 25r2 = 6r Solving -2 + 5r + 25r2 = 6r Solving for variable 'r'. Reorder the terms: -2 + 5r + -6r + 25r2 = 6r + -6r Combine like terms: 5r + -6r = -1r -2 + -1r + 25r2 = 6r + -6r Combine like terms: 6r + -6r = 0 -2 + -1r + 25r2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.08 + -0.04r + r2 = 0 Move the constant term to the right: Add '0.08' to each side of the equation. -0.08 + -0.04r + 0.08 + r2 = 0 + 0.08 Reorder the terms: -0.08 + 0.08 + -0.04r + r2 = 0 + 0.08 Combine like terms: -0.08 + 0.08 = 0.00 0.00 + -0.04r + r2 = 0 + 0.08 -0.04r + r2 = 0 + 0.08 Combine like terms: 0 + 0.08 = 0.08 -0.04r + r2 = 0.08 The r term is -0.04r. Take half its coefficient (-0.02). Square it (0.0004) and add it to both sides. Add '0.0004' to each side of the equation. -0.04r + 0.0004 + r2 = 0.08 + 0.0004 Reorder the terms: 0.0004 + -0.04r + r2 = 0.08 + 0.0004 Combine like terms: 0.08 + 0.0004 = 0.0804 0.0004 + -0.04r + r2 = 0.0804 Factor a perfect square on the left side: (r + -0.02)(r + -0.02) = 0.0804 Calculate the square root of the right side: 0.283548938 Break this problem into two subproblems by setting (r + -0.02) equal to 0.283548938 and -0.283548938.Subproblem 1
r + -0.02 = 0.283548938 Simplifying r + -0.02 = 0.283548938 Reorder the terms: -0.02 + r = 0.283548938 Solving -0.02 + r = 0.283548938 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.02' to each side of the equation. -0.02 + 0.02 + r = 0.283548938 + 0.02 Combine like terms: -0.02 + 0.02 = 0.00 0.00 + r = 0.283548938 + 0.02 r = 0.283548938 + 0.02 Combine like terms: 0.283548938 + 0.02 = 0.303548938 r = 0.303548938 Simplifying r = 0.303548938Subproblem 2
r + -0.02 = -0.283548938 Simplifying r + -0.02 = -0.283548938 Reorder the terms: -0.02 + r = -0.283548938 Solving -0.02 + r = -0.283548938 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.02' to each side of the equation. -0.02 + 0.02 + r = -0.283548938 + 0.02 Combine like terms: -0.02 + 0.02 = 0.00 0.00 + r = -0.283548938 + 0.02 r = -0.283548938 + 0.02 Combine like terms: -0.283548938 + 0.02 = -0.263548938 r = -0.263548938 Simplifying r = -0.263548938Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.303548938, -0.263548938}
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